How to Find GCF of 261/340, 9889/682?

GCF of 261/340, 9889/682

Created By : Veerendra
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023

Use our free GCF of Fractions Calculator tool to compute the GCF of 261/340, 9889/682 i.e 29/115940 easily. The following is the detailed procedure to determine the greatest common factor of fractions 261/340, 9889/682.

Enter two or more fractions separated by "commas"

Ex: 2/3, 5/7 or 3/5, 5/9, 7/3

What is the GCF of 261/340,9889/682?

Given fractions are 261/340,9889/682

To find the GCF of fractions, we have to find the GCF of numerator numbers and LCM of denominator numbers. Its formula is given by

GCF of Fraction = Greatest Common Factor of Numerator/Least Common Multiple of Denominators

In the fractions 261/340,9889/682, numerators are 261,9889

Denominators are 340,682

The GCF of 261,9889 is 29 .

LCM of 340,682 is 115940.

The greatest common factor of 261/340,9889/682 = [GCF of 261,9889]/[LCM of 340,682]= 29/115940

Therefore, the GCF of 261/340,9889/682 is 29/115940.

Greatest Common Factor of 261,9889

To find the highest common factor of 261,9889, we have to find the factors of both numbers and list the highest common factor.

The factors of 261 are 1, 3, 9, 29, 87, 261

The factors of 9889 are 1, 11, 29, 31, 319, 341, 899, 9889

The HCF of 261,9889 is 29.

Lets's calculate GCF of 261,9889

Greatest Common Factor (GCF) of 261,9889 By Common Division

29	261, 9889
	9, 341

∴ So the GCF of the given numbers is 29 = 29

Greatest Common Factor of 261,9889 By Matching Biggest Common Factor Method

Now, list down the factors of 261

1,3,9,29,87,261

Now, list down the factors of 9889

1,11,29,31,319,341,899,9889

Greatest Common Factor

We found the factors 261,9889 . The biggest common factor number is the GCF number.
So the greatest common factor 261,9889 is 29.

Lets's calculate LCM of 340,682

Lowest Common Multiple of 340,682 using Common Division

2	340, 682
	170, 341

∴ So the LCM of the given numbers is 2 x 170 x 341 = 115940

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 29/115940

Therefore, the GCF of Fractions 261/340,9889/682 is 29/115940

Least Common Multiple of 340,682 with GCF Formula

The formula of LCM is LCM(a₁,a₂,a₃....,a_n) = ( a₁ × a₂ × a₃ × .... × a_n) / GCF(a₁,a₂,a₃....,a_n) x common factors(if more than 2 numbers have common factors).

We need to calculate greatest common factor of 340,682 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(340,682) = 2

common factors(in case of two or more numbers have common factors) = 1

GCF(340,682) x common factors =2 x 1 = 2

LCM(340,682) = ( 340 × 682 ) / 2

LCM(340,682) = 231880 / 2

LCM(340,682) = 115940

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FAQs on GCF of Fractions of 261/340, 9889/682

1. What is the HCF of 261,9889?

The HCF of 261,9889 is 29

2. What is the GCF of a fraction?

The GCF of a fraction is defined as the greatest fraction that divides exactly into 2 or more fractions.

3. How to find GCF in Fractions?

Answer: GCF of fractions can be found using the simple formula GCF of Fractions = GCF of Numerators/LCM of Denominators.

4. What is the GCF of Fractions for 261/340, 9889/682?

Answer: GCF of Numerators as per given numbers 261/340, 9889/682 is

GCF of Numerators i.e. for 261,9889 is 29

LCM of denominators i.e. for 340,682 is 115940.

Thus, GCF of Fractions is 29/115940.Finally, GCF of Fractions for 261/340, 9889/682 is 29/115940.